In the following questions, the symbols- &, @, % and $ are used with the following meanings as illustrated below. Study the following information and answer the given questions. In each of the questions given below statements are followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements regarding commonly known facts.

A@B means “All A are B”
A&B means “Only a few A are B”
A$B means “No A is B”
A%B means “Some A is B”

Statement: F%J$G&C@E
I. All C can never be F
II. Some G is not E
III. All F being G is not a possibility
IV. Some J being E is a possibility

The correct option is Both III and IV.

Step 1: Decode the given symbols and statements

• A@B means "All A are B"
• A&B means "Only a few A are B" (This implies both "Some A are B" and "Some A are not B")
• A$B means "No A is B"
• A%B means "Some A is B"

Given Statement: F%J$G&C@E

Breaking down the statement into individual relationships:
1. F % J ⇒ Some F are J.
2. J $ G ⇒ No J is G.
3. G & C ⇒ Only a few G are C (Implies: Some G are C, and Some G are not C).
4. C @ E ⇒ All C are E.

Step 2: Analyze each conclusion

Conclusion I: All C can never be F
• There is no direct or negative relation given between C and F.
• Since there is no restriction, it is possible for All C to be F.
• Therefore, saying "All C can never be F" (a definite negative statement) does not logically follow. Thus, Conclusion I does not follow.

Conclusion II: Some G is not E
• We know that All C are E, and Some G are C.
• However, the portion of G that is not C could potentially still be E.
• Therefore, "Some G is not E" is not a definite true statement. Thus, Conclusion II does not follow.

Conclusion III: All F being G is not a possibility
• We know that Some F are J (from F%J).
• We also know that No J is G (from J$G).
• Since the portion of F that is J can never be G, it is impossible for All F to be G.
• Since "All F being G" is impossible, stating that it "is not a possibility" is correct and logically follows. Thus, Conclusion III follows.

Conclusion IV: Some J being E is a possibility
• There is no negative relation between J and E (J is only restricted from being G).
• Since there is no restriction prohibiting overlap between J and E, "Some J being E" is a valid possibility.
• Thus, Conclusion IV follows.

Conclusion:
Hence, only conclusions III and IV logically follow.